Forrester won the European Youth Team Championship in 1978 and the European Team Championship in 1991. The European Team Championship win was in partnership with Andrew Robson, with whom he played for seven years. The pair also won the Cap Gemini and the Sunday Times-Macallan. Around that time he was regarded, by the English Bridge Union, as England's number one player.

With 38 caps for England in the Camrose Trophy, Forrester is second only to the late John Armstrong. with 40.

Forrester has won the Gold Cup, the premier British teams competition, 10 times in 1983, 1986, 1989, 1990, 1992, 1993, 2000, 2001, 2007 and 2009. He won the Spring Foursomes in 1983, 1996, 1999 and 2009.

In 2010, he won the Brighton Four Stars A Final, with team mates Alexander Allfrey, Andrew Robson and Peter Crouch.